Question

Hello, May I please get some assistance with this homework question? I posted an image below Q1

Answer 1

ANSWERS

a) 5

b) 6

c) -2

d) -1

Step-by-step explanation

The composition of two functions is equivalent to,

`(g\circ f)(x)=g(f(x))`

a) To find (g o f)(4) we have to find g(f(4)). In the graph, we can see that the value of f(x) at x = 4 is -1,

`(g\circ f)(4)=g(f(4))=g(-1)`

Then, g(x) at x = -1 is 5.

Hence,

`(g\circ f)(4)=5`

b) Similarly,

`(g\circ f)(0)=g(f(0))`

f(x) at x = 0 is 1,

`g(f(0))=g(1)`

And g(x) at x = 1 is 6.

Hence,

`(g\circ f)(0)=6`

c) In this case, first, we have to find the value of g(x),

`(f\circ g)(3)=f(g(3))`

The value of g(x) at x = 3 is 3,

`f(g(3))=f(3)`

And the value of f(x) at x = 3 is -2.

Hence,

`(f\circ g)(3)=-2`

d) Similarly,

`(f\circ g)(4)=f(g(4))`

The value of g(x) at x = 4 is 4,

`f(g(4))=f(4)`

And the value of f(x) at x = 4 is -1.

Hence,

`(f\circ g)(4)=-1`