How to Multiply and Dividing Functions? (+FREE Worksheet!)

Multiplying and dividing functions are similar to multiplying and dividing polynomials. Learn how to multiply and divide functions in this post.

Step by step guide to Multiplying and Dividing Functions

• Just like we can multiply and divide numbers, we can multiply and divide functions. For example, if we had functions $$f$$ and $$g$$, we could create two new functions: $$f × g$$, and $$\frac{f}{g}$$.

Multiplying and Dividing Functions – Example 1:

$$g(x)=x+1, f(x)=x-2$$, Find: $$(g.f)(2)$$

Solution:

$$(g.f)(x)=g(x).f(x)=(x+1)(x-2)=x^2-2x+x-2=x^2-x-2$$
Substitute $$x$$ with $$2$$:
$$(g.f)(2)=x^2-x-2=(2)^2-2-2=4-2-2=4-4=0$$

Multiplying and Dividing Functions – Example 2:

$$f(x)=x-2, h(x)=x+8$$, Find: $$(\frac{f}{h})(-1)$$

Solution:

$$(\frac{f}{h})(x)=\frac{f(x)}{h(x)} =\frac{x-2}{x+8}$$
Substitute $$x$$ with $$-1: (\frac{f}{h})(-1)=\frac{x-2}{x+8}=\frac{(-1)-2}{(-1)+8}=\frac{-3}{7}=-\frac{3}{7}$$

Multiplying and Dividing Functions – Example 3:

$$g(x)=-x-2, f(x)=2x+1$$, Find: $$(g.f)$$$$(x)$$

Solution:

$$(g.f)(x)=g(x).f(x)=(-x-2)(2x+1)=-2x^2-x-4x-2=-2x^2-5x-2$$

Multiplying and Dividing Functions – Example 4:

$$f(x)=x+4, h(x)=5x-2$$, Find: $$(\frac{f}{h})$$$$(x)$$

Solution:

$$(\frac{f}{h})(x)=\frac{f(x)}{h(x)} =\frac{x+4}{5x-2}$$

Exercises for Multiplying and Dividing Functions

Perform the indicated operation.

• $$\color{blue}{g(a) = 2a – 1 \\ h(a) = 3a – 3 \\ Find \ (g.h)(– 4) } \\\$$
• $$\color{blue}{f(x) = 2x^3 – 5x^2 \\ g(x) = 2x – 1 \\ Find \ (f.g)(x)} \\\$$
• $$\color{blue}{g(t) = t^2 + 3 \\ h(t) = 4t – 3 \\ Find \ (g.h)(– 1)} \\\$$
• $$\color{blue}{g(n) = n^2 + 4 + 2n \\ h(n) = – 3n + 2 \\ Find \ (g.h)(1)} \\\$$
• $$\color{blue}{g(a) = 3a + 2 \\ f(a) = 2a – 4 \\ Find (\frac{g}{f})(3) } \\\$$
• $$\color{blue}{f(x) = 3x – 1 \\ g(x) = x^2 – x \\ Find \ (\frac{f}{g})(x)}$$

• $$\color{blue}{135}$$
• $$\color{blue}{4x^4 – 12x^3 + 5x^2}$$
• $$\color{blue}{-28}$$
• $$\color{blue}{-7}$$
• $$\color{blue}{\frac{11}{2}} \\\$$
• $$\color{blue}{\frac{3x-1}{x^2-x}}$$

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