Evaluate Functions - Pre-Calculus

Card 0 of 40

Question

Given and , evaluate .

Answer

We are given two functions and asked to find f(h(7)).

I would begin by finding h(7)

Now that we know h(7), we go ahead and plug it into f(x).

$f(0)=5\cdot 0^2-13\cdot 0+8=8$

So our final answer is simply 8.

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Question

Solve the function. $\frac{10x^2-10}{x-1}=0$

Answer

Determine the domain of $\frac{10x^2-10}{x-1}=0$ .

$x\neq1$

Multiply on both sides of the equation to cancel the denominator and divide the equation by ten.

$x= \pm1$

Since the domain states that $x\neq1$ , the only possible answer is .

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Question

Solve for :

Answer

Rewrite so that the exponential variable is isolated.

Reconvert to a similar base. Use exponents to redefine the terms.

Since all terms are of the same base, use the property of log to eliminate the base on both sides of the equation.

Solve for .

$x=\frac{1}{2}$

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Question

Determine the value of of the function

$f(x)=\sqrt{71-x}$

Answer

In order to determine the value of of the function we set The value becomes

$f(7)=\sqrt{71-7}=\sqrt{64}=8$

As such

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Question

Evaluate the following function when

$f(t)=5^{3t-18}+5^t-t^2$

Answer

Evaluate the following function when

$f(t)=5^{3t-18}+5^t-t^2$

To evaluate this function, simply plug-in 6 for t and simplify:

$f(6)=5^{3(6)-18}+5^6-(6)^2=1+15625-36=15590$

So our answer is:

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Question

Find the value of the following function when

$g(x)=\frac{2x^2-4x+5}{x^4-16}$

Answer

Find the value of the following function when

$g(x)=\frac{2x^2-4x+5}{x^4-16}$

To evaluate this function, plug in 2 for x everywhere it arises and simplify:

$g(x)=\frac{2(2)^2-4(2)+5}{(2)^4-16}=\frac{5}{0}=\mbox{undefined}$

So our answer must be undefined, because we cannot divide by

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Question

Find the value of when $t=\frac{3\pi}{4}$

$g(t)=5\cos(t)-5\sin(t)$

Answer

Find the value of when $t=\frac{3\pi}{4}$

$g(t)=5\cos(t)-5\sin(t)$

To evaluate this expression, plug in the given value of everywhere you see a and simplify:

$g(\frac{3\pi}{4})=5\cos(\frac{3\pi}{4})-5\sin(\frac{3\pi}{4})=5(\frac{-\sqrt{2}}{2}-\frac{\sqrt{2}}{2})=5(\frac{-2\sqrt{2}}{2})=-5\sqrt{2}$

$5(\frac{-2\sqrt{2}}{2})=-5\sqrt{2}$

So our answer is:

$-5\sqrt{2}$

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Question

Find the difference quotient of the function .

Answer

Difference quotient equation is

$\frac{f(x+h)-f(x)}{h}$ and

.

Now plug in the appropriate terms into the equation and simplify:

$\ \frac{f(x+h)-f(x)}{h}\ \=\frac{3(x+h)^2-2(x+h)-5-(3x^2-2x-5)}{h}\ \=\frac{3(x^2+2xh+h^2)-2x-2h-5-3x^2+2x+5}{h}\ \=\frac{3x^2+6xh+3h^2-2x-2h-5-3x^2+2x+5}{h}\ \=\frac{6xh+3h^2-2h}{h}\ \=\frac{h(3h+6x-2)}{h}\ \=3h+6x-2$

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Question

If , what is ?

Answer

In order to evaluate this function, simply substitute the value of as a replacement of .

Simplify using the order of operations.

The answer is:

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Question

Evaluate for $x=\frac{3\pi}{4}$ .

Answer

We evaluate the function when $x=\frac{3\pi}{4}$ .

$f(\frac{3\pi}{4})=sin^2(\frac{3\pi}{4})=(\frac{\sqrt{2}}{2})^2=\frac{2}{4}=\frac{1}{2}$

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Question

Given and , evaluate .

Answer

We are given two functions and asked to find f(h(7)).

I would begin by finding h(7)

Now that we know h(7), we go ahead and plug it into f(x).

$f(0)=5\cdot 0^2-13\cdot 0+8=8$

So our final answer is simply 8.

Compare your answer with the correct one above

Question

Solve the function. $\frac{10x^2-10}{x-1}=0$

Answer

Determine the domain of $\frac{10x^2-10}{x-1}=0$ .

$x\neq1$

Multiply on both sides of the equation to cancel the denominator and divide the equation by ten.

$x= \pm1$

Since the domain states that $x\neq1$ , the only possible answer is .

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Question

Solve for :

Answer

Rewrite so that the exponential variable is isolated.

Reconvert to a similar base. Use exponents to redefine the terms.

Since all terms are of the same base, use the property of log to eliminate the base on both sides of the equation.

Solve for .

$x=\frac{1}{2}$

Compare your answer with the correct one above

Question

Determine the value of of the function

$f(x)=\sqrt{71-x}$

Answer

In order to determine the value of of the function we set The value becomes

$f(7)=\sqrt{71-7}=\sqrt{64}=8$

As such

Compare your answer with the correct one above

Question

Evaluate the following function when

$f(t)=5^{3t-18}+5^t-t^2$

Answer

Evaluate the following function when

$f(t)=5^{3t-18}+5^t-t^2$

To evaluate this function, simply plug-in 6 for t and simplify:

$f(6)=5^{3(6)-18}+5^6-(6)^2=1+15625-36=15590$

So our answer is:

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Question

Evaluate for $x=\frac{3\pi}{4}$ .

Answer

We evaluate the function when $x=\frac{3\pi}{4}$ .

$f(\frac{3\pi}{4})=sin^2(\frac{3\pi}{4})=(\frac{\sqrt{2}}{2})^2=\frac{2}{4}=\frac{1}{2}$

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Question

Find the value of the following function when

$g(x)=\frac{2x^2-4x+5}{x^4-16}$

Answer

Find the value of the following function when

$g(x)=\frac{2x^2-4x+5}{x^4-16}$

To evaluate this function, plug in 2 for x everywhere it arises and simplify:

$g(x)=\frac{2(2)^2-4(2)+5}{(2)^4-16}=\frac{5}{0}=\mbox{undefined}$

So our answer must be undefined, because we cannot divide by

Compare your answer with the correct one above

Question

Find the value of when $t=\frac{3\pi}{4}$

$g(t)=5\cos(t)-5\sin(t)$

Answer

Find the value of when $t=\frac{3\pi}{4}$

$g(t)=5\cos(t)-5\sin(t)$

To evaluate this expression, plug in the given value of everywhere you see a and simplify:

$g(\frac{3\pi}{4})=5\cos(\frac{3\pi}{4})-5\sin(\frac{3\pi}{4})=5(\frac{-\sqrt{2}}{2}-\frac{\sqrt{2}}{2})=5(\frac{-2\sqrt{2}}{2})=-5\sqrt{2}$

$5(\frac{-2\sqrt{2}}{2})=-5\sqrt{2}$

So our answer is:

$-5\sqrt{2}$

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Question

Find the difference quotient of the function .

Answer

Difference quotient equation is

$\frac{f(x+h)-f(x)}{h}$ and

.

Now plug in the appropriate terms into the equation and simplify:

$\ \frac{f(x+h)-f(x)}{h}\ \=\frac{3(x+h)^2-2(x+h)-5-(3x^2-2x-5)}{h}\ \=\frac{3(x^2+2xh+h^2)-2x-2h-5-3x^2+2x+5}{h}\ \=\frac{3x^2+6xh+3h^2-2x-2h-5-3x^2+2x+5}{h}\ \=\frac{6xh+3h^2-2h}{h}\ \=\frac{h(3h+6x-2)}{h}\ \=3h+6x-2$

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Question

If , what is ?

Answer

In order to evaluate this function, simply substitute the value of as a replacement of .

Simplify using the order of operations.

The answer is:

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