if f(x)= -2x + 3 and g(x) = 2x^2 +4x - 3, what is g(f(x))?

Question

plz help with pre cal

Answer 1

g(f(x)) means to put the f(x) function into the g equation everywhere you see an x.

So...
g(f(x))
= 2(-2x + 3)^2 + 4(-2x + 3) - 3
= 2(4x^2 - 12x + 9) - 8x + 12 - 3
= 8x^2 - 24x + 18 - 8x + 9
= 8x^2 - 32x + 27

Answer 2

2

Answer 3

stick to the order of operations while doing any difficulty, PEDMAS parenthesis, exponents, branch, multiplication, addition and then subtraction first distribute the three so 4x + 6 - 3x = 8 - 2x next are there any exponents? no, so flow directly to multiplication or branch, there is none now all thats left is addition and subtraction upload the like words x's with x's and numbers with humbers so im including the 4x and -3 x+6=8-2x now oyu can the two upload the 2x to the two sides considering the fact which you ought to get numbers on one area and variables on the different so now im gonna upload the 2x so the -2x will flow away now its 3x+6=8 now im gonna subtract the 6 from the two sides now im left with 3x=2 now all you ought to do is divide the three so as that the x is on my own so which you get x= 2/3 and to confirm if it somewhat is powerful you purely plug the two/3 decrease back into the unique equation and the two sides ought to equivalent one yet another 4(2/3)+3(2-(2/3))=8-2(2/3) 20/3= 20/3

Answer 4

gf(x) means taking the 'f' function and were an 'x' is seen in the 'g' function, substituting in the whole of the 'f' function.

g(f(x)) =2(-2x+ 3)^2 + 4(-2x +3) - 3
g(f(x)) = 2[4x^2 -12x +9] - 8x +12 - 3
g(f(x)) = 8x^2 -24x +18 - 8x + 12 -3
g(f(x)) = 8x^2 -32x +27

The top line is the critical line, the rest is a tidying-up exercise.

Note also f(g(x)) is different.
f(g(x)) = -2(2x^2 +4x - 3) + 3
f(g(x)) = -4x^2 - 8x +6 - 3
f(g(x)) = -4x^2 - 8x + 3 -- a completely different result.

Answer 5

if f(x)= -2x + 3 and g(x) = 2x^2 +4x - 3, what is g(f(x))
g(f(x)) = 2(-2x+3)^2+4(-2x+3) -3
= 2(4x^2-12x +9) -8x +12 -3
= 8x^2 -24x +18 -8x +12 - 3
= 8x^2 -32x + 27

Answer 6

g(f(x))=2(-2x+3)^2+4(-2x+3)-3
=2(4x^2-12x+9)-8x+12-3
=8x^2-24x+18-8x+9
=8x^2-32x+27

Answer 7

g(f(x))
= 2f^2+4f-3
= 2(-2x+3)^2+4(-2x+3) - 3
= 8x^2 - 32x + 27
--------
Ideas: Substitute f for x in g(x) first.

Answer 8

pay attention in class, do ur homework