Evaluate Functions

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Pre-Calculus › Evaluate Functions

Questions 1 - 10

1

Determine the value of of the function

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

$f(7)=\sqrt{78}$

$f(7),, \textsc{dne}$

Explanation

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

2

Evaluate the following function when

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

Explanation

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:

3

Find the value of the following function when

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

The function is undefined at

Explanation

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

4

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

$\pm1$

$\pm \frac{1}{10}$

Explanation

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

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

$x= \pm1$

Since the domain states that , the only possible answer is .

5

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

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

$-5\sqrt{2}$

Explanation

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:

$-5\sqrt{2}$

6

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

$\frac{1}{2}$

$\frac{\sqrt2}{2}$

$-\frac{1}{2}$

$\frac{3}{4}$

Explanation

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

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

7

Given and , evaluate .

Explanation

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.

8

Find the difference quotient of the function .

Explanation

Difference quotient equation is

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

.

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

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

9

Solve for :

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{4}$

$\frac{2}{3}$

$\frac{4}{9}$

Explanation

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 .

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

10

If , what is ?

Explanation

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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