Question

Find fog and gof if f(x)=|x+1| and g(x)=2x-1

Answer 1

Find fog and gof if f(x)=|x+1| and g(x)=2x-1

Answer 2

$Given \: f(x) = |x+1| \: --(1)$

$and \: g(x) = 2x - 1 \: ---(2)$

$i) fog(x) = f\big(g(x)\big)$

$= f(2x-1) \: [ From \: (2) ]$

$= | (2x-1) + 1| \: [ From \: (1) ]$

$= | 2x - 1 + 1 |$

$= | 2x |$

$\therefore \red{ fog(x)} \green {= | 2x |}$

$ii) gof(x) = g\big(f(x)\big)$

$= g\big( |x+1|\big) \: [ From \: (1) ]$

$= 2|x+1| - 1 \: [ From \: (2) ]$

$\therefore \red{ gof(x) }\green {= 2|x+1| - 1}$

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