Algebra 2 Question - Function's Inverse

Question

Which function’s inverse has the greatest value at x=4?

g(x)=10^x+2
k(x)=ln⁡⁡(x+3)
f(x)=log⁡⁡(x−1)
h(x)=e^x+2

Answer 1

Function G(x)

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4 = 10^x + 2

 

2 = 10^x

 

log 2 = log 10^x

 

1og 2 = x log 10

 

x = log 2/ log 10 = 0.30103

 

 

 

Function K(x)

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4 = ln(x+3)

 

e^4 = x+3

 

e^4 - 3 = x = 54.59815

 

 

Function F(x)

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4 = log(x-1)

e^4 = x-1

 

e^4 + 1 = x <--- this will be LARGER than the previous

                          so it's the largest thus far

 

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Function H(x)

 

4 = e^x + 2

 

2 = e^x

 

ln 2 = x = 0.693147

 

Winner:

K(x) = ln(x+3)