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The range of the function f(x)=9^x-3^x+1 is

The range of the function f(x)=9^x-3^x+1 is

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1 Answers

vikas askiitian expert
509 Points
10 years ago

f(x) = 9x - 3x + 1

f(x) = (32x) - 3x + 1

let 3x = t

f(x) = t2 - t + 1

f(x) = t2 - t +1/4 - 1/4 + 1

f(x) = (t-1/2)2 + 1-1/4

f(x) = (t-1/2)2 + 3/4

square of any number cannot be less than 0 so minimum value of this function

is 3/4 when (t-1/2)2 = 0

maximum value can be infinity

so its range is [3/4 , infinity)

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