If f(x) = 4^(x) - 2^(x + 1) + 5, then ra...

If f(x) `= 4^(x) - 2^(x + 1) + 5`, then range of f(x) is

A

R

B

`[5,oo)`

C

`[4, oo)`

D

`[0, oo)`

Verified by Experts

The correct Answer is:

C

`f(x)= 4^(x)-2^(x+1) +5=(2^(x))^(2) -2.2^(x)+5`
`=(2^(x)-1)^(2)+4`
`:. (2^(x) -1)^(2) ge 0`
`f(x)=(2^(x)-1)^(2)+4 ge 4`. Hence range `[4, oo)`

Similar Questions

Explore conceptually related problems

If f(x)=cos^(-1)(x) and g(x)=x^(2) , then range of f(g(x)) is)

If f(x) = (sin^2x + 4sinx + 5)/(2 sin ^2x + 8 sin x + 8) , then range of f(x) is

If f(x)+2f(1-x)=x^(2)+1,AA x in R, then the range of f is :

The range of f(x)=x^(2)+x+1 is

Let f (x) =(x^(2) +x-1)/(x ^(2) - x+1) , In above problem, the range of f (x) AA x in [-1, 1] is:

If f(x) = (x - 1)(x - 2)(x - 3)(x - 4)(x - 5) , then the value of f' (5) is equal to

f(x)=log_(3)(5+4x-x^(2)) . find the range of f(x).

A={x/x in R,x!=0,-4<=x<=4 and f:A rarr R is defined by f(x)=(|x|)/(x) for x in A. Then the range of f is