What is the range of a^x ?

The range of a^x is (f(x)>0\land (0 1))\lor (f(x)=1\land a=1)

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range of a^x

range

a^{x}

(f (x) > 0 and (0 < a < 1 or a > 1)) or (f (x) = 1 and a = 1)

Interval Notation

(f (x) \in (0, \infty) \cap (a \in (0, 1) \cup a \in (1, \infty))) \cup (f (x) = 1 \cap a = 1)

Solution steps

The range of an exponential function of the form

c \cdot n^{a x + b} + k

(f (x) > k and (0 < n < 1 or n > 1)) or (f (x) = c + k and n = 1)

n = a, c = 1, k = 0

Apply general form:

(f (x) > 0 and (0 < a < 1 or a > 1)) or (f (x) = 1 and a = 1)

f (x) = (x - 1) e^{- x}

\frac{1}{x + 3}

f (x) = \frac{( - 2 x ^{2} )}{x ^{2} + 4 x - 5}

f (x) = \frac{7}{8} - x

f (x) = - x^{3} + 27 x - 52

What is the range of a^x ?
The range of a^x is (f(x)>0\land (0<a<1\lor a>1))\lor (f(x)=1\land a=1)