If-f-x-5-g-2x-1-Find-2f-1-x-A-g-1-x-11-D-g-1-x-2-6-B-g-1-x-9-E-g-1-2x-6-C-g-1-x-6-

Question Number 13099 by Joel577 last updated on 14/May/17

If f (x + 5) = g (2 x - 1)

Find 2 f^{- 1} (x)

(A) g^{- 1} (x) + 11 (D) g^{- 1} (x / 2) + 6

(B) g^{- 1} (x) + 9 (E) g^{- 1} (2 x) + 6

(C) g^{- 1} (x) + 6

Answered by 433 last updated on 14/May/17

h (x) = x + 5 & k (x) = 2 x - 1

f o h = g o k

f = {g o k o h}^{- 1}

f^{- 1} = {h o k}^{- 1} g^{- 1}

2 f^{- 1} = 2 ({h o k}^{- 1} g^{- 1})

k^{- 1} (x) = \frac{x + 1}{2}

2 f^{- 1} (x) = 2 h (k^{- 1} (g^{- 1}) (x)

= 2 h (\frac{g^{- 1} (x) + 1}{2})

= 2 (\frac{g^{- 1} (x) + 1}{2} + 5) = g^{- 1} (x) + 1 + 10

= g^{- 1} (x) + 11

Commented by Joel577 last updated on 15/May/17

t h a n k y o u v e r y m u c h

Answered by mrW1 last updated on 14/May/17

f (x + 5) = g (2 x - 1) = u

\Rightarrow x + 5 = f^{- 1} (u) \dots (i)

\Rightarrow 2 x - 1 = g^{- 1} (u) \dots (i i)

2 \times (i) - (i i) :

\Rightarrow 11 = 2 f^{- 1} (u) - g^{- 1} (u)

\Rightarrow 2 f^{- 1} (u) = g^{- 1} (u) + 11

\Rightarrow 2 f^{- 1} (x) = g^{- 1} (x) + 11

\Rightarrow A n s w e r (A)

Commented by RasheedSindhi last updated on 14/May/17

E asy n simple!

Commented by Joel577 last updated on 15/May/17

t h a n k y o u v e r y m u c h

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