What is the range of b^x ?

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

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range of b^x

range

b^{x}

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

Interval Notation

(f (x) \in (0, \infty) \cap (b \in (0, 1) \cup b \in (1, \infty))) \cup (f (x) = 1 \cap b = 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 = b, c = 1, k = 0

Apply general form:

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

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