# Let f be the function be defined by f(x)=5^((2x^2)

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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

• Let f be the function be defined by f(x)=5^((2x^2) -

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

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