bemath-Given-f-x-2x-3-g-f-x-2x-1-find-f-g-2-

Question Number 106707 by bemath last updated on 06/Aug/20

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G iven {\begin{cases} f (x) = 2 x + 3 \\ (g \circ f) (x) = 2 x - 1 \end{cases}

find (f \circ g) (2) .

Answered by john santu last updated on 06/Aug/20

Answered by mathmax by abdo last updated on 06/Aug/20

f (x) = 2 x + 3 and g (f (x)) = 2 x - 1 \Rightarrow g (2 x + 3) = 2 x - 1

let 2 x + 3 = t \Rightarrow x = \frac{t - 3}{2} \Rightarrow g (t) = 2 (\frac{t - 3}{2}) - 1 = t - 4

g (t) = t - 4 \Rightarrow fog (2) = f (g (2)) = f (- 2) = - 4 + 3 = - 1 \Rightarrow

fog (2) = - 1