College Algebra

Question

1) Find the inverse of the function f(x) = 8x + 16.

 

2(Determine if the following functions are inverses of each other:
f(x) = 7x + 14
g(x) = (1/7)x - 2

 

3)Write the exponential equation y = 5x in logarithmic form.

4) Write the logarithmic equation log7x = y in exponential form.

5(Use the change-of-base formula to convert x=log390 to common logarithms. Then use a calculator to round the value of x to the nearest thousandth.

Answer 1

(1) y = 8x + 16

x = 8y + 16 <--- x and y switch places
x-16 = 8y <--- solves for y0

(x-16)/8 = y


(2) f(g(x)) = 7 ( (1/7)x - 2) + 14 =
7 * (1/7) X - 14 + 14 =
[7 * (1/7)]X + (14 - 14) =
1X + 0 =
X

g(f(x)) = (1/7) ( 7x + 14) - 2

(1/7)(7x) + (1/7)(14) - 2
x + 2 - 2 =
x

(3) y = 5x is not an exponential function.
y = 5^x is an exponential function.

ln y = ln 5^x = x*ln 5


(4) log 7x = y

7x = 10^y

x = 10^y/7


(5) change of base formula : logA z = logB z / logB a

(6) x = log 390 ---> log390 = logE 390 / logE 10

= ln 390 / ln 10

Per Calculator log10 390 = 2.59106460703..... = ln 390/ln 10