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Question
f\left(x\right)=\ln{\left(x-5\right)}
Function
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Find the inverse
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Evaluate the derivative
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Find the domain
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\text{Find the }x\text{-intercept/zero}
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Find the y-intercept
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Find the critical numbers
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Find the local extrema
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Find the increasing or decreasing interval
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Find the range
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Find the vertical asymptotes
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Find the horizontal asymptotes
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Find the oblique asymptotes
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Determine if even, odd or neither
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Find the stationary points
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Find the inflection points
More methods
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f^{-1}\left(x\right) = e^{x}+5
Evaluate
f\left(x\right)=\ln{\left(x-5\right)}
\text{In the equation for }f\left(x\right)\text{,replace }f\left(x\right)\text{ with }y
y=\ln{\left(x-5\right)}
\text{Interchange }x\text{ and }y
x=\ln{\left(y-5\right)}
Swap the sides of the equation
\ln{\left(y-5\right)}=x
\text{Convert the logarithm into exponential form using the fact that }\log_{a}{x}=b\text{ is equal to }x=a^{b}
y-5=e^{x}
Move the constant to the right-hand side and change its sign
y=e^{x}+5
Solution
f^{-1}\left(x\right) = e^{x}+5
Show Solutions
Testing for symmetry
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Testing for symmetry about the origin
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Testing for symmetry about the x-axis
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Testing for symmetry about the y-axis
\textrm{Not symmetry with respect to the origin}
Evaluate
f\left(x\right)=\ln{\left(x-5\right)}
Rewrite the function using the appropriate notation
y=\ln{\left(x-5\right)}
\text{To test if the graph of }y=\ln{\left(x-5\right)}\text{ is symmetry with respect to the origin,substitute -x for x and -y for y}
-y=\ln{\left(-x-5\right)}
Change the signs both sides
y=-\ln{\left(-x-5\right)}
Solution
\textrm{Not symmetry with respect to the origin}
Show Solutions
Graph
