Question
Let f be the function be defined by f(x)=5^((2x^2)-1)^(1/2)
find the range of f without using a calculator
find the range of f without using a calculator
Answers
Reiny
f(x)=5^((2x^2)-1)^(1/2)
= 5^(x^2 - 1/2)
x^2 is always positive, so the smallest exponent that 5 could have is -1/2 when x = 0
for any other value of x, x^2 - 1/2 is greater than -1/2
we know 5^(-1/2) = 1/√5 or √5/5
so the range is y ≥ √5/5
= 5^(x^2 - 1/2)
x^2 is always positive, so the smallest exponent that 5 could have is -1/2 when x = 0
for any other value of x, x^2 - 1/2 is greater than -1/2
we know 5^(-1/2) = 1/√5 or √5/5
so the range is y ≥ √5/5