If f(x)=2x+1, and g(x)=x-3, then g(f(x))= ( ?)x + (?)

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Answer 1 · 2018-06-20T04:13:56

$g o f (x) = g (f (x)) = 2 (x - 1)$ $gof(x)=g(f(x))=2(x-1)$

Here,

$color(red)(f(x)=2x+1...to(1) and g(x)=x-3....to(2)$

We assume that , $R_fsube D_g and gof$ exist.

$gof(x)=g(f(x))$

$color(white)(gof(x))=g(2x+1)$ .... $color(red)(touse (1)$

$color(white)(gof(x))=g(m)$ .....where , $color(blue)(m=2x+1$

$color(white)(gof(x))=m-3$ ..... $color(red)(touse(2)$

$color(white)(gof(x))=(2x+1)-3$ ,,,,,where , $color(blue)(m=2x+1$

$color(white)(gof(x))=2x-2$

$gof(x)=2(x-1)$

Answer : $color(orange)((2))x+color(orange)((-2))$