Question

let f(x)=x+8 and g(x)=x^2-6x-7. find f(g(2))

Answer 1

very similar to the last one
again it takes two steps, not one

Answer 2

first you need to find \(g(2)\)

Answer 3

ok i did the problem and got 10 am i wrong because i could try again

Answer 4

ok lets take it step by step

\[g(x)=x^2-6x-7\] so
\[g(2)=2^2-6\times 2-7\]

Answer 5

when you compute that number you get
\[2^2-6\times 2-7=4-12-7=-8-7=-15\] and that is just step one
we still have to do step 2

Answer 6

oh ok so what do we do for step 2?

Answer 7

for step 2 we have to compute
\[f(-15)\]

Answer 8

\[f(x)=x+8\] so \[f(-15)=-15+8\]

Answer 9

so its just 8 now

Answer 10

because we minus the 15

Answer 11

no
what is \(-15+8\) ?

Answer 12

-7

Answer 13

right! and that is your final answer
lets put it all together in one line

Answer 14

\[f(g(2))=f(-15)=-7\]

Answer 15

oh wow thanks i have another one if you could be so kind as to help me :)

Answer 16

sure what is it?

Answer 17

let f(x)=9x-2 and g(x)=-x+3. find f(g(x))

Answer 18

ok for this one we have no numbers so we have to do something a bit different

Answer 19

\[f(x)=9x-2,g(x)=-x+3\]

Answer 20

\[f(g(x))\] always work from the inside out, it is easier
in this case \(g(x)=-x+3\) so replace \(g(x)\) by \(-x+3\) to get
\[f(g(x))=f(-x+3)\]

Answer 21

then
\[f(x)=9x-2\] or
\[f(\heartsuit)=9\heartsuit-2\] we are going to replace \(\heartsuit\) by \((-x+3)\) to get
\[f(\heartsuit)=f(-x+3)=9(-x+3)-2\]

Answer 22

so is the answer -9x-2

Answer 23

now we have to clean this up with a bit of algebra
\[9(-x+3)-2=-9x+27-2=-9x+25\]

Answer 24

don't forget the distributive law here

Answer 25

\[9(-x+3)=9\times (-x)+9\times 3=-9x+27\]

Answer 26

so it would be -9x+27

Answer 27

then subtract the 2 to get a final answer of \(-9x+25\)

Answer 28

oh ok i get that i have another one but its a little different and i need some help

Answer 29

k

Answer 30

let f(x)=-4x+7 and g(x)=10x-6 find f(g(x))

Answer 31

no it is not really different
\[f(g(x))=f(10x-6)=-4(10x-6)+7\] is the first two steps

Answer 32

then some algebra to clean it up

Answer 33

ok

Answer 34

you got the algebra?

Answer 35

my algebra says the first part should be -40x

Answer 36

but im not sure about the last part

Answer 37

distribute the \(-4\) through the parentheses first to get
\[-4(10x-6)+7=-40x+24-7\]

Answer 38

then since \(24-7=17\) you end with
\[-40x+17\]

Answer 39

then wat do we do?

Answer 40

wouldnt it be -40x+24

Answer 41

no because we have that \(-7\) out at the end
when you distribute, yes, you get \(-40x+24\) but there is also the \(-7\) giving a final answer of
\[-40x+17\]

Answer 42

ok thanks :)

Answer 43

yw