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

Option B is correct

Explanation:

We need to find g(h(f(x))

We first find h(f(x))

f(x) = x-3/x

Putting value of f(x) in place of x in h(x)

h(x) = 2x+1

h(f(x)) = 2(x-3/x) + 1

= 2(x-3/x) + 1

= 2x -6 /x +1

= 2x-6 +x/x

= 3x-6/x

Now, putting value of h(f(x)) in g(x)

g(x) = x+3

g(h(f(x)))= (3x-6/x) + 3

= 3x-6/x + 3

= 3x-6+3x/x

= 6x-6/x

So, Option B is correct.