Question 1140124
y = 3^x
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domain of this function is all real numbers, the function does not cross the x-axis, therefore there are no roots (x-intercepts)
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here is a graph of the equation y = 3^x
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{{{ graph( 300, 200, -2, 2, -1, 10, 3^x) }}}
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the real solution for the inverse, interchange x and y and solve for y
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x = 3^y
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take the natural logarithm of both sides of =
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ln(x) = y * ln(3)
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y = ln(x)/ln(3)
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f^(-1) (x) = ln(x)/ln(3) for x > 0
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here is a graph of the inverse
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{{{ graph( 600, 500, -2.731, 2.731, -2.5, 1, ln(x)/ln(3)) }}}
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