Question

Evaluate the composite function f(g(h(-3))) using the given functions:

- f(x) = 3x + 3
- g(x) = 2x - 1
- h(x) = x² + 1

Then, determine the value of the expression.

A. -48
B. 170
C. 60
D. -168

Answer 1

Step-by-step explanation:

hello :

f(g(h(-3))) :

h(-3) = (-3)²+1 = 10

g(h(-3))= g(10)=2(10)-1=19

f(g(h(-3))) = f(19)=3(19)+3 =60

f(g(h(-3))) =60

Answer 2

To find the value of the composite function f(g(h(-3))), evaluate each function step by step, starting with h(-3), then g(10), and finally f(19), which gives the result 60, corresponding to option C.

Step-by-step explanation:

The composite function f(g(h(-3))) needs to be evaluated step by step, starting from the innermost function to the outermost. First, let's find h(-3):

h(x) = x² + 1

h(-3) = (-3)² + 1 = 9 + 1 = 10.

Next, we evaluate g(h(-3)) or g(10):

g(x) = 2x - 1

g(10) = 2(10) - 1 = 20 - 1 = 19.

Finally, we evaluate f(g(h(-3))) or f(19):

f(x) = 3x + 3

f(19) = 3(19) + 3 = 57 + 3 = 60.

Therefore, the value of the expression f(g(h(-3))) is 60, which corresponds to option C.