Question

use f(x)=5x+2 and g(x)=3-x. what is the value of f(g(-1)) and g(f(-1))?

Answer 1

Answer:

f(g(-1)) = 22

g(f(-1))=6

Step-by-step explanation:

We are given

$f(x)=5x+2 \\g(x)=3-x$

We need to find f(g(-1)) and g(f(-1))

Finding f(g(-1))

First we will find f(g(x)) i.e

$f(g(x))=5(3-x)+2\\f(g(x))=15-5x+2\\f(g(x))=-5x+17$

Now finding f(g(-1)) by putting x=-1

$f(g(x))=-5x+17\\Put \ x=-1\\f(g(-1))=-5(-1)+17\\f(g(-1))=5+17\\f(g(-1))=22$

So, f(g(-1)) = 22

Finding g(f(-1))

First we will find g(f(x)) i.e

$g(f(x))=3-(5x+2)\\g(f(x))=3-5x-2\\g(f(x))=-5x+1$

Now finding g(f(-1)) by putting x=-1

$g(f(x))=-5x+1\\Put \ x = -1\\g(f(-1))=-5(-1)+1\\g(f(-1))=5+1\\g(f(-1))=6$

So, g(f(-1))=6