given three functions f, g, and h, define (f ∘ g ∘ h)(x)=fg(h(x)). find (f ∘ g ∘ h)(1) if f(x)=6x - 9…

given three functions f, g, and h, define (f ∘ g ∘ h)(x)=fg(h(x)). find (f ∘ g ∘ h)(1) if f(x)=6x - 9, g(x)=1/x, and h(x)=√(x + 3). (f ∘ g ∘ h)(1)= (simplify your answer.)

given three functions f, g, and h, define (f ∘ g ∘ h)(x)=fg(h(x)). find (f ∘ g ∘ h)(1) if f(x)=6x - 9, g(x)=1/x, and h(x)=√(x + 3). (f ∘ g ∘ h)(1)= (simplify your answer.)

Answer

Answer:

$-3$

Explanation:

Step1: Calculate $h(1)$

$h(1)=\sqrt{1 + 3}=\sqrt{4}=2$

Step2: Calculate $g(h(1))$

Since $h(1)=2$, then $g(h(1))=g(2)=\frac{1}{2}$

Step3: Calculate $f(g(h(1)))$

Since $g(h(1))=\frac{1}{2}$, then $f(g(h(1)))=f(\frac{1}{2})=6\times\frac{1}{2}-9 = 3 - 9=-3$