What is the range of $f(x) = -3^x + 4$ ?

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Answer 1 · 2015-05-06T16:50:21

Write $y=-3^x+4$

$=>3^x=4-y$

Take $ln$ of both sides

$=>ln3^x=ln(4-y)$

$=>x=ln(4-y)/ln3$

Now notice that $(4-y)$ cannot be negative nor zero!

$=>4-y>0 =>y<4$

Hence the range of $f(x)$ is $f(x)<4$

What is the range of f(x) = -3^x + 4f(x) = -3^x + 4?