If f(x) = 2x -5  and g(x) = lnx + 8x  find fog(1)

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have f(x) = 2x -5  and g(x) = lnx + 8x  and we have to find fog(1).

fog(x) = f(g(x))

=> f( ln x + 8x)

=> 2*(ln x + 8x) - 5

Therefore fog(1)

=> 2*(ln 1 + 8*1) - 5

=> 2*( 0 + 8) - 5

=> 2* 8 - 5

=> 16 - 5

=> 11

Therefore fog(1) = 11

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the functions:

f(x) = 2x-5

g(x) = lnx + 8x

We need to find fog(1)

First we will determine the function fog(x)

==> fog(x) = f(g(x))

                 = f( lnx + 8x)

                  = 2(lnx + 8x) -5

                    = 2lnx + 16x - 5

==> fog(x) = 2lnx + 16x  -5

Now we will substitute with x = 1

==> fog(1) = 2ln1 + 16*1 -5

                 = 2*0 + 16 -5 = 11

==> fog(1) = 11

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

f(x) = 2x-5 and g(x) = lnx+8x.

To find fog(1).

fog(x) = f(g(x))

fog(x) = 2g(x) -5.

fog(x) = 2(lnx+8x) - 5.

fog(1) = 2(ln1+8*1)-5

fog(1) = 2(0+8)-5, as ln1 = 0.

fog(1) = 16-5 = 11.

fog(1) = 11.

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