f(x) = and g(x) = 3x – 2. If f(g(x)) = 1, what is the value of x ?

Question

f(x) = \frac{2-x}{5} and  g(x) = 3x - 2 . If  f(g(x)) = 1 , what is the value of x?

(A)  \frac{-5}{3}

(B)  \frac{-1}{3}

(C)  \frac{2}{3}

(D) 1

(E)  \frac{5}{3}

D3N0 · Answer

Ans: B
f(g(x)) =  /5=1
so 4-3x=5 ; x= -(1/3)

CareerGeek · Answer

f(g(x)) = 1
-->  \frac{2 - (3x - 2)}{5}  = 1
-->  \frac{4 - 3x}{5}  = 1
--> 3x = -1
--> x = -1/3

IMO Option B

BrushMyQuant · Answer

Given that  f(x) = \frac{2-x}{5} and  g(x) = 3x - 2  and  f(g(x)) = 1  and we need to find the value of x

f(g(x)) -> substituting value of  g(x) = 3x - 2  we get

=> f(g(x)) = f(3x - 2)

To find f(3x - 2) we need to compare what is inside the ( ) in f(3x - 2) and  f(x) = \frac{2-x}{5}

=> We need to substitute x with 3x - 2 in  f(x) = \frac{2-x}{5}  to get the value of f(3x - 2)

=>  f(3x - 2) = \frac{2 - (3x - 2)}{5}  =  \frac{4 - 3x}{5}

=> f(g(x)) =  \frac{4 - 3x}{5}  = 1 (given)
=> 4 - 3x = 1*5 = 5
=> 3x = 4 - 5 = -1
=> x =  \frac{-1}{3}

So,  Answer will be B 
Hope it helps!

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