TOLONG JAWAB AKAN KU KASIH 30 POINT!

f(x) = 2x+ 5 dan g(x) = x − 2

Carilah: (gof)−1(x) = (f−1o g−1)(x)

TOLONG JAWAB AKAN KU KASIH 30 POINT!

$f(x) = 2x + 5 \ y = 2x + 5 \ 2x = y - 5 \ x = frac{y - 5}{2} \ {f}^{ - 1} (x) = frac{x - 5}{2}$

$g(x) = x - 2 \ y = x - 2 \ x = y + 2 \ {g}^{ - 1} (x) = x + 2$

$(gof)(x) = g(f(x)) \ (gof)(x) =f(x) - 2 \ (gof)(x) =(2x + 5) - 2 \ (gof)(x) =2x + 3 \ y = 2x + 3 \ 2x = y - 3 \ x = frac{y - 3}{2} \ {(gof)}^{ - 1} (x) = frac{x - 3}{2}$

$( {f}^{ - 1} o {g}^{ - 1} )(x) = {f}^{ - 1} ( {g}^{ - 1} (x)) \ ( {f}^{ - 1} o {g}^{ - 1} )(x) = frac{ {g}^{ - 1}(x) - 5 }{2} \ ( {f}^{ - 1} o {g}^{ - 1} )(x) = frac{(x + 2) - 5}{2} \ ( {f}^{ - 1} o {g}^{ - 1} )(x) = frac{x - 3}{2}$

Jadi

${(gof)}^{ - 1} (x) = ( {f}^{ - 1} o {g}^{ - 1} )(x) = frac{x - 3}{2}$