Question

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

Answer 1

Answer:

1. f(x)=x+7

2. f(x)=1.2x

Step-by-step 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:

$f(x)=1.2x$