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Let f(x) be a function whose domain is [-5, 7] and g(x) = |2x+5|. Then, the domain of fog(x), is a)[-5,1] b)[-4,0] c)[-6,1] d)none of these While solving this question we take – 7 is less than or equal to |2x + 5| is less than or equal to 7. Why don’t we then consider – 5 as the lower limit and 5 as the upper limit.

 
Let f(x) be a function  whose domain is [-5, 7] and g(x) = |2x+5|. Then, the domain  of fog(x), is 
a)[-5,1]
b)[-4,0]
c)[-6,1]
d)none of these
 
While solving this question we take  – 7 is less than or equal to |2x + 5| is less than or equal to 7.
Why don’t we then consider – 5 as the lower limit and 5 as the upper limit.

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1 Answers

Deepak Kumar Shringi
askIITians Faculty 4404 Points
5 years ago
look you are finding domain of fog now so now whole g(x) will work as x only
earlier domain was from [-5,7] but now as its g(x) so g(x) should be from [-5,7] so you will write
-5 < g(x) ,<7 ( its more than equal to)

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