Functions Question 593
If $ f(x)=3x+10 $ , $ g(x)=x^{2}-1 $ , then $ {{(gof)}^{-1}} $ is equal to
[UPSEAT 2001]
Options:
A) $ {{( \frac{x-7}{3} )}^{1/2}} $
B) $ {{( \frac{x+7}{3} )}^{1/2}} $
C) $ {{( \frac{x-3}{7} )}^{1/2}} $
D) $ {{( \frac{x+3}{7} )}^{1/2}} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ f(x)=3x+10 $ and $ g(x)=x^{2}-1 $
Þ $ f,o,g=f(g(x))=3(g(x))+10 $ = $ 3(x^{2}-1)+10 $ = $ 3x^{2}-3+10 $ = $ 3x^{2}+7 $ …..(i)
Let $ 3x^{2}+7=y $
Þ $ 3x^{2}=y-7 $
Þ $ x^{2}=\frac{y-7}{3}\Rightarrow x={{( \frac{y-7}{3} )}^{1/2}} $
We know that $ f(x)=y $ , then $ x={f^{-1}}(y) $
so $ {{(fog)}^{-1}}={{( \frac{x-7}{3} )}^{1/2}} $ .
BETA
