Question

Hey Friends!! solve this quest!
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Q) If f:R->R and g:R->R are defined by f(x)=2x+3 and g(x)=x²+7, then the values of x such that g(f(x))=8 are:
Options are:
i) 1,2
ii) -1,2
iii) -1,-2
iv) 1,-2
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Please answer it accurately and BEWARE OF SPAMMING!!

Answer 1

$\red{\bold{ANSWER}}$

$\rm{-1\:\:,-2}$

$\mathbb{EXPLANATION}$

$\rm{F:R\rightarrow\:R}$

$\rm{F\left(x\right)=2x+3}$

$\boxed{\mathbb{AND}}$

$\rm{G:R\rightarrow\:R}$

$\rm{G\left(x\right)=x^2+7}$

$\underline{\mathbb{GIVEN}}$

$\rm{G\left(F\left(x\right)\right)=8}$

$\rm{G\left(2x+3\right)=8}$

$\rm{\left(\left(2x+3\right)^2+7\right)=8}$

$\rm{4x^2+9+12x+7-8=0}$

$\rm{4x^2+12x+8=0}$

$\rm{x^2+3x+2=0}$

$\rm{x^2+2x+x+2=0}$

$\rm{x\left(x+2\right)+1\left(x+2\right)=0}$

$\rm{\left(x+2\right)\times\left(x+1\right)=0}$

$\rm{x=-2\:\:OR\:\:x=-1}$

$\therefore$ $\rm{x=-2,-1}$

$\boxed{\rm{\mathbb{HENCE,\:OPTION\:THIRD\:IS\:CORRECT}}}$

Answer 2

Answer:

hope it helps you.............