Question

If f(x)=(4x-3) / 2 and g(x) =(2x+3) / 4, which of the following is true?

A f(g(x)) =1
B f(g (x)) = 0
C f(g(x))=-1
D f(g(x)) = x

Answer 1

f(g(x))= x

Explanation:

f(x)=(4x-3)/2

g(x) =(2x+3)/4

f(g(x)) means use the value obtained from g(x) in the equation defined by f(x). Since g(x) =(2x+3)/4, we can substitute (2x+3)/4 in place of the x in f(x).

If f(x)=(4x-3)/2 then use the expression (2x+3)/4 in place of "x" in (4x-3)/2

f(x) = (4x-3)/2

g(x) = (2x+3)/4

f(g(x))=(4((2x+3)/4)-3)/2

f(g(x))=(((8x+12)/4)-3)/2

f(g(x))= (2x+3-3)/2

f(g(x))= 2x/2

f(g(x))= x