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Precalculus : Add, Subtract, Multiply, and Divide Functions

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Example Questions

Example Question #23 : Algebra Of Functions

If $f(x)=\frac{4x-1}{x^2}$ and g(x)=x+1 , find $f\cdot g(x)$ .

Possible Answers:

$\frac{4x+3}{x^2-2x+1}$

$\frac{x+3}{x^2+2x+1}$

$\frac{4x+3}{2x+1}$

$\frac{4x+3}{x^2+2x+1}$

$\frac{4x+3}{x^2+2x-1}$

Correct answer:

$\frac{4x+3}{x^2+2x+1}$

Explanation:

To solve this problem, you must plug in the g function to wherever you see x in the f function. When you plug that in, it looks like this: $\frac{4(x+1)-1}{(x+1)^2}$ . Then simplify so that your answer is: $\frac{4x+3}{x^2+2x+1}$ .

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Example Question #24 : Algebra Of Functions

Find $\left(\frac{f}{g}\right)(x)$ given $f(x)=\frac{1}{x^3}$ and $g(x)=\frac{1}{x^2}$ .

Possible Answers:

$(\frac{f}{g})(x)=\frac{1}{x^2}$

$(\frac{f}{g})(x)=\frac{1}{x^5}$

$(\frac{f}{g})(x)=\frac{1}{x}$

The answer is not present.

$(\frac{f}{g})(x)=\frac{1}{x^6}$

Correct answer:

$(\frac{f}{g})(x)=\frac{1}{x}$

Explanation:

The problem is asking to find the composite function that results when f(x) is divided by g(x).

When dividing fractions, it is important to remember to multiply by the inverse.

$\left(\frac{f}{g}\right)(x)=\frac{\frac{1}{x^3}}{\frac{1}{x^2}}=\frac{1}{x^3}*\frac{x^2}{1}=\frac{1}{x}$

Cross cancel the exponents leaving only one "x" in the bottom.

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Precalculus : Add, Subtract, Multiply, and Divide Functions

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #23 : Algebra Of Functions

Example Question #24 : Algebra Of Functions

All Precalculus Resources

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