Signature 1 Let fx 2 Find the inverse function f1x r 2 Find

Signature: 1) Let f(x)= 2. Find the inverse function f-1(x). r- 2) Find the exact value of a) log,(16) . 100 3) Solve log, (4x-7)-2 for x

1) f(x) =1/(x-2)

f^-1(x) : plug x=y and y=x

y = 1/(x-2)

x = 1/(y-2) ---> xy -2x =1

y= (1+2x)/x

f^-1(x) = (1 +2x)/x

2) ln2(16)

now 16 = 2^4

So,log2(16) = log2(2^4) = 4*log2(2)

= 4*log2/log2 = 4

log100 = log(10^2) = 2*log10

= 2*1 =2

ln(sqrt(e) = lne^1/2 = 1/2*lne

=(1/2)lne/lne = 1/2

3) ln3(4x -7) = 2

(4x -7) = 2^3

4x -7 = 8

4x = 15

x= 15/4