LET F(X)=7X+1 AND LET G(X)= X-1/7, COMPUTE F o g(x) and g o f(x). what do your answer mean?

LET F(X)=7X+1 AND LET G(X)= X-1/7, COMPUTE F o g(x) and g o f(x). what do your answer mean?

another problem is
use the one to one property to solve the equation for x
1.. 3^x+1=27
2...... 2^x-3=16
3... 2^x-2=1/32
4.... (1/5)^x+1=125
5... e^2x-1= e4
6... e^x2+6=e^5x

please help any steps to follow or easy way to learn those exercise or any video

1 Answer
Sean
Apr 29, 2018

Please see below.

Explanation:

.

You need to enclose the #(x-1)# in #g(x)# in parentheses. The same goes for all the exponents in problems #1.# through #6.#. Otherwise, you would have completely different problems.

#f(x)=7x+1#

#g(x)=(x-1)/7#

#f@g(x)=f(g(x))=7((x-1)/7)+1=x-1+1=x#

#g@f(x)=g(f(x))=(7x+1-1)/7=(7x)/7=x#

This means that #f(x)# and #g(x)# are inverse functions of each other.

Using one to one property, we solve the following:

#color(red)1.# #color(red)(3^(x+1)=27)#

#3^(x+1)=3^3#

One to one property means the only way this can be true is if:

#x+1=3#

#x=2#

#color(red)2.# #color(red)(2^(x-3)=16)#

#2^(x-3)=2^4#

#x-3=4#

#x=7#

#color(red)3.# #color(red)(2^(x-2)=1/32)#

#2^(x-2)=1/2^5=2^(-5)#

#x-2=-5#

#x=-3#

#color(red)4.# #color(red)((1/5)^(x+1)=125)#

#(5^(-1))^(x+1)=5^3#

#5^(-x-1)=5^3#

#-x-1=3#

#x=-4#

#color(red)5.# #color(red)(e^(2x-1)=e^4)#

#2x-1=4#

#2x=5#

#x=5/2#

#color(red)6.# #color(red)(e^(x^2+6)=e^(5x))#

#x^2+6=5x#

#x^2-5x+6=0#

#(x-6)(x+1)=0#

#x=6 and -1#

Here are some videos to watch to learn how to solve these types of problems:

How to solve exponential problems using one to one property

How to solve exponential problems using one to one property

Related questions
Impact of this question
2379 views around the world
You can reuse this answer
Creative Commons License