Multiplying and dividing functions is similary 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 \(\frac{f}{g}\).

### 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 \(2\):

\((g.f)(x)=x^2-x-2=(2)^2-2-2=4-2-2=0 \)

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

### Example 3:

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

**Solution:**

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

### Example 4:

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

**Solution:**

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

## Exercises

### Perform the indicated operation.

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

### Download Multiplying and Dividing Functions Worksheet

## Answers

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