MHT CET202311 May 2023Evening ShiftMathematicsFunctionsActual

If f (x)= 3 x+4 5 x-7 and g (x)= 7 x+4 5 x-3 , then f ( g (x))=

Options

Ax^3+1 x^2+2
B41 x
Cg(f(x))
D5 x-7 41

Correct answer

C. g(f(x))

Step-by-step solution

aligned f(g(x)) & =f ( 7 x+4 5 x-3 ) & = 3 ( 7 x+4 5 x-3 )+4 5 ( 7 x+4 5 x-3 )-7 & = 21 x+12+20 x-12 35 x+20-35 x+21 & = 41 x 41 & =x aligned aligned & Now, g ( f (x))= g ( 3 x+4 5 x-7 ) &= 7 ( 3 x+4 5 x-7 )+4 5 ( 3 x+4 5 x-7 )-3 &= 21 x+28+20 x-28 15 x+20-15 x+21 &= 41 x 41 &=x & f ( g (x))= g ( f (x)) aligned

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