Question

if f(x)=x-3/x, g(x)=x+3, and h(x)=2x+1, what is (g*h*f)(x).

A. 3x-6/x
B. 6x-6/x
C. 2x+4/2x+7
D. 4x-3/x

Answer 1

Answer = (g*h*f)(x) = 4x-3/x

Answer 2

Answer:

Option B - 6x-6/x

Step-by-step explanation:

Given : If $f(x)=\frac{x-3}{x}, g(x)=x+3,h(x)=2x+1$.

To find : What is the value of  $(g(h(f)))(x)$

Solution :

$(g(h(f)))(x)=g(h(f(x)))$

i.e, substitute the value of f(x) in h(x) and then put that h(x) in g(x).

$g(h(f(x)))=g(h(\frac{x-3}{x}))$

$g(h(f(x)))=g(2(\frac{x-3}{x})+1)$

$g(h(f(x)))=(2(\frac{x-3}{x})+1)+3$

Solving the RHS,

$=(2(\frac{x-3}{x})+1)+3$

$=(\frac{2x-6}{x})+1)+3$

$=(\frac{2x-6+x}{x})+3$

$=\frac{3x-6}{x}+3$

$=\frac{3x-6+3x}{x}$

$=\frac{6x-6}{x}$

Therefore, The value of $(g(h(f)))(x)=\frac{6x-6}{x}$

Hence, Option B is correct.