Question

composite function worksheet for credit. work must be neat and answer must be circled. f(x)=2x - 1, g(x)=3x, and h(x)=x² + 1. compute the following: 2. f(h(7)) 3. (g∘h)(24) 5. h(g(f(5))) 6. g(f(h(-6))) 8. g(3a)

Explanation:

Step1: Find h(7)

Given $h(x)=x^{2}+1$, substitute $x = 7$: $h(7)=7^{2}+1=49 + 1=50$.

Step2: Find f(h(7))

Given $f(x)=2x - 1$, substitute $x = h(7)=50$: $f(h(7))=f(50)=2\times50-1=100 - 1 = 99$.

Step3: Find h(24) for (g∘h)(24)

Given $h(x)=x^{2}+1$, substitute $x = 24$: $h(24)=24^{2}+1=576+1 = 577$.

Step4: Find (g∘h)(24)

Given $g(x)=3x$, substitute $x = h(24)=577$: $(g\circ h)(24)=g(h(24))=3\times577 = 1731$.

Step5: Find f(5) for h(g(f(5)))

Given $f(x)=2x - 1$, substitute $x = 5$: $f(5)=2\times5-1=9$.

Step6: Find g(f(5))

Given $g(x)=3x$, substitute $x = f(5)=9$: $g(f(5))=3\times9 = 27$.

Step7: Find h(g(f(5)))

Given $h(x)=x^{2}+1$, substitute $x = g(f(5))=27$: $h(g(f(5)))=27^{2}+1=729 + 1=730$.

Step8: Find h(-6) for g(f(h(-6)))

Given $h(x)=x^{2}+1$, substitute $x=-6$: $h(-6)=(-6)^{2}+1=36 + 1=37$.

Step9: Find f(h(-6))

Given $f(x)=2x - 1$, substitute $x = h(-6)=37$: $f(h(-6))=2\times37-1=74 - 1=73$.

Step10: Find g(f(h(-6)))

Given $g(x)=3x$, substitute $x = f(h(-6))=73$: $g(f(h(-6)))=3\times73 = 219$.

Step11: Find g(3a)

Given $g(x)=3x$, substitute $x = 3a$: $g(3a)=3\times3a=9a$.

Answer:

1. $99$
2. $1731$
3. $730$
4. $219$
5. $9a$