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The functions g and h such that

 

g(x)=2x+5                h(x)=ax+b

 

where a and b are constants.

 

h(3)=26 and g^-1(21)=h(1)

 

Find the value of a and the value of b.

 

smileysmileysmiley

 May 18, 2018
 #1
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g(x)  = 2x + 5

h(x)  = ax + b

If  h (3)  = 26     we have that   26  =a(3) + b  ⇒    3a + b  = 26   (1)

 

And   g-1 (x)   is     [ x - 5] / 2

So  g-1(21)   is    [ 21 - 5] /2   = 16 /2   =  8

 

So  g-1(21)  = 8  =  h(1)   which implies that

 

8 = a(1) + b    ⇒  a + b  = 8    (2)

 

So...we have the system

 

3a + b  = 26

a + b  =  8          subtract the second equation from the first

 

2a  = 18

a = 9

 

And    a + b  = 8     so   9 + b  = 8   ⇒   b  = -1

 

So  the function is

 

y = 9x  - 1

 

And a = 9   and  b  = -1

 

 

 

cool cool cool

 May 18, 2018

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