Question

Can someone help me with these two questions? I learned them but I completely forgot how to solve them. Thanks! <3

Answer 1

f( g(x) ), you first solve g(x) and the output is then the input for f(x)

g(-3) = (-3) -7
g(-3) = -10.

Next, we use this result to evaluate f(x):
f(g(-3)) = f(-10) = 2 * (-10) + 5
f(g(-3)) = -20 + 5 = -15

Answer 2

Okay, so the answer would be 25?

Answer 3

minus twenty plus 5 = minus 15

Answer 4

Okay, -15, thank you :) For number 8 how would you set up the equation? First I did g(2)=2+4/3
g2=6/3
g2=2
-2 -2
g=0
Is this correct for the first part?

Answer 5

yes however you can't subtract the 2 from the sides
g(2) = 2 is the last you can get

Answer 6

cause g(0) would actually be 3/4 or something when x=0

Answer 7

Oh okay, soo g=2. How would I do the second part of the problem? I don't really understand how to write the second equation out.

Answer 8

insert g=2 for every input x=g():
\[x^{2}+2*x + 3 =(2)^{2}+2*(2)+3\]

Answer 9

the x in f(x) is already the "next x" - the result from g(x)

Answer 10

it's actually like \[f(g) = g ^{2}+2*g+3\]

Answer 11

Ohhhh okay, so it's 11. That makes sense. Just one more question about what you said "yes however you can't subtract the 2 from the sides
g(2) = 2 is the last you can get"
let's say it was g(5)=10. Would I subtract the 5 in this case?

Answer 12

you are not allowed to subtract "function inputs" when subtracting both sides.
if you subtract 5 from both sides, you must subtract from whatever that function returns

g(5)-5 = 10-5
g(5)-5 = 5
...is valid.

sin(90°) = 1, you can't subtract and say sin(89°) = 0

Answer 13

Okay, I just thought you were supposed to get the "g" by itself.

Answer 14

because g is a function you can't get it by itself. it is always an "instruction" on how to process whatever it is given. this would however be possible if g was a variable

Answer 15

Okay thank you so much! I really appreciate the help