gof(x) — Let g(x) = x - 3 2 be y. So, fog(x) = f(y) = 2y + 3. Substituting y = x - 3 2 , we get fog(x) = (x – 3) + 3 = x = [ ( 2 x + 3 ) - 3 ] 2 = gof(x)

CAT 1994 — QA Question 37

Composite FunctionsEasy

Passage / Data

Answer the next 4 questions based on the information given below:

If f (x) = 2x + 3 and g(x) = $\frac{x - 3}{2},$ then

fog(x) is equal to

Answer & solution

Correct answer: gof(x)

A
1
gof(x)
C
$\frac{15 x + 9}{16 x - 5}$
D
$\frac{1}{x}$

Solution

Let g(x) = $\frac{x - 3}{2}$ be y. So, fog(x) = f(y) = 2y + 3.
Substituting y = $\frac{x - 3}{2},$ we get

fog(x) = (x – 3) + 3 = x = $\frac{[(2 x + 3) - 3]}{2}$ = gof(x)

CAT 1994 — QA Question 37

Answer & solution

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