Question

1. Find f(x) if it is known that f(x+5)=x+12.

2. Find f(x) if it is known that f(x−5)=1.2x−6.

Answer 1

1. f(x)=x+7

2. f(x)=1.2x

Explanation:

1. If f(x+5)=x+12, then substitute

`t=x+5\Rightarrow x=t-5`

Hence,

`f(t)=(t-5)+12\\ \\f(t)=t+7`

Now change t into x:

`f(x)=x+7`

2. If f(x-5)=1.2x-6, then substitute

`t=x-5\Rightarrow x=t+5`

Hence,

`f(t)=1.2(t+5)-6\\ \\f(t)=1.2t+6-6\\ \\f(t)=1.2t`

Now change t into x:

`f(x)=1.2x`