Learn how to add and subtract Functions by finding and combining like terms.

## Related Topics

- How to Solve Composition of Functions
- How to Multiply and Dividing Functions
- How to Solve Function Notation
- How to find Inverse of a Function

## Step by step guide to Adding and Subtracting Functions

- Just like we can add and subtract numbers, we can add and subtract functions. For example, if we had functions \(f(x) \) and \(g(x)\), we could create two new functions: \((f + g)(x)\) and \((f – g)(x)\).
- When functions contain polynomials, find the like terms and combine them to add or subtract functions.
- When evaluating functions, substitute the value of the input and find the value of the function.

### Adding and Subtracting Functions – Example 1:

\(g(a)=a-1, f(a)=a+5\), Find: \((g+f)(-1)\)

**Solution:**

\((g+f)(a)=g(a)+f(a), Then: (g+f)(a)=a-1+a+5=2a+4\)

Substitute \(a \) with \(-1: (g+f)(a)=2a+4=2(-1)+4=-2+4=2 \)

### Adding and Subtracting Functions – Example 2:

\(f(x)=3x-3, g(x)=x-5\), Find: \((f-g)(3)\)

**Solution:**

\((f-g)(x)=f(x)-g(x), then: (f-g)(x)=3x-3-(x-5)=3x-3-x+5

=2x+2\)

Substitute \(x\) with \(3: (f-g)(1)=2(3)+2=8\)

### Adding and Subtracting Functions – Example 3:

\(f(x)=2x+4, g(x)=x+3\), Find: \((f-g)(1)\)

**Solution:**

\((f-g)(x)=f(x)-g(x)\), then: \((f-g)(x)=2x+4-(x+3)

=2x+4-x-3=x+1 \)

Substitute \(x\) with \(1: (f-g)(1)=1+1=2\)

### Adding and Subtracting Functions – Example 4:

\(g(a)=2a-1, f(a)=-a-4\), Find: \((g+f)(-1)\)

**Solution:**

\((g+f)(a)=g(a)+f(a), Then: (g+f)(a)=2a-1-a-4=a-5\)

Substitute \(a \) with \(-1: (g+f)(a)=a-5=-1-5=-6 \)

## Exercises for Adding and Subtracting Functions

### Perform the indicated operation.

- \(\color{blue}{h(t) = 2t + 1, \\ g(t) = 2t + 2, \\ Find \ (h – g)(t)} \\\ \)
- \(\color{blue}{g(a) = – 3a – 3, \\ f(a) = a^2 + 5, \\ Find \ (g – f)(a)} \\\ \)
- \(\color{blue}{g(x) = 2x – 5, \\ h(x) = 4x + 5, \\ Find \ g(3) – h(3)} \\\ \)
- \(\color{blue}{h(3) = 3x + 3, \\ g(x) = – 4x + 1, \\ Find \ (h + g)(10)} \\\ \)
- \(\color{blue}{f(x) = 4x – 3, \\ g(x) = x^3 + 2x, \\ Find \ (f – g)(4)} \\\ \)
- \(\color{blue}{h(n) = 4n + 5, \\ g(n) = 3n + 4, \\ Find \ (h – g)(n)}\)

### Download Adding and Subtracting Functions Worksheet

- \(\color{blue}{-1}\)
- \(\color{blue}{–a^2 – 3a – 8}\)
- \(\color{blue}{-16}\)
- \(\color{blue}{-6}\)
- \(\color{blue}{-59}\)
- \(\color{blue}{n+1}\)