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

Question

asked Dec 6, 2023 51.4k views

1 Answer

Self · Answer 1 · 2023-12-11T15:49:27+0000

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,

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,

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,

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

Hence,

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