Respuesta :
Answer:
y = lnx + 4.
y = log 5 (x + 9).
y = 10^(x-13).
Step-by-step explanation:
To find the inverse you need to make x the subject of the equation:
y = e^(x - 4)
By the definition of a logarithm:
x - 4 = ln y
x = ln y + 4
Now swap x's and y's :-
The inverse is y = lnx + 4.
y = 5^x - 9
Swap x and y:
x = 5^y - 9
5^y = x + 9
The inverse is y = log5( x + 9).
y = 13 + log x
log x = y - 13
x = 10^(y-13)
The inverse is y = 10^(x-13).
Answer: [tex]\bold{f^{-1}(x)=ln(x)+4}[/tex]
Step-by-step explanation:
Find the inverse by swapping the x's and y's and then solving for y.
[tex]y=e^{x-4}\\\\\\\text{swap the x and y}:\\x=e^{y-4}\\\\\\\text{apply ln to both sides (to eliminate e)}:\\ln(x)=ln(e^{y-4})\quad \rightarrow \quad ln(x)=y-4\\\\\\\text{add 4 to both sides}:\\ln(x)+4=y\\\\\\\text{Therefore, the inverse is: }f^{-1}(x)=ln(x)+4[/tex]
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Answer: [tex]\bold{f^{-1}(x)=log_5(x+9)}[/tex]
Step-by-step explanation:
Find the inverse by swapping the x's and y's and then solving for y.
[tex]y=5^x-9\\\\\\\text{swap the x and y}:\\x=5^y-9\\\\\\\text{add 9 to both sides}:\\x+9=5^y\\\\\\\text{Use the exponent-to-log conversion rule (aka apply }log_5\ \text{to both sides)}:\\log_5(x+9)=y\\\\\\\text{Therefore, the inverse is: }f^{-1}(x)=log_5(x+9)[/tex]
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Answer: [tex]\bold{f^{-1}(x)=10^{x-13}}[/tex]
Step-by-step explanation:
Find the inverse by swapping the x's and y's and then solving for y.
[tex]y=13+log(x)\\\\\\\text{swap the x and y}:\\x=13+log(y)\\\\\\\text{subtract 13 from both sides}:\\x-13=log(y)\\\\\\\text{Use the log-to-exponent conversion rule (note: log = }log_{10})\\10^{x-13}=y\\\\\\\text{Therefore, the inverse is: }f^{-1}(x)=10^{x-13}[/tex]
