Question

Find the range of
f(x)= {e^3(x-2)} +7

Answer 1

We have to find the range of f(x) = $e^{3(x-2)}+7$.

let y = f(x) = $e^{3(x-2)}+7$

⇒y-7 = $e^{3(x-2)}$

taking log base e we get,

⇒ln(y - 7) = 3(x - 2)

⇒ln(y - 7)/3 = x - 2

⇒ln(y - 7)/3 + 2 = x

⇒x = f(y) = ln(y - 7)/3 + 2

now find the domain of f(y), you will get the range of function, f(x).

for log to be defined, (y - 7) > 0

domain of f(y) , y > 7

I.e., The range of function, f(x) ∈ (7, ∞)

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