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Composite Functions, need a quick lookover!

f(x) = -x, g(x) = 1-x2

gf(x) = g(-x)

=>1-(-x)2

What have I done wrong? I'm trying to find ranges using this and any range I get from the domain is wrong :frown:

I've never liked these :frown:
Reply 1
Avatar for rbnphlp
rbnphlp
11
Loz17
f(x) = -x, g(x) = 1-x2

gf(x) = g(-x)

=>-(1-x)2

What have I done wrong? I'm trying to find ranges using this and any range I get from the domain is wrong :frown:

I've never liked these :frown:

I dont understand how you got that

if you put f(x)into g(x) you get

1-(-x)^2=1-x^2

Spoiler

Reply 2
Avatar for LadySmythe
LadySmythe
OP
19
Sorry, my typo. I got 1-(-x)2

But won't that go to 1 + x2?
Reply 3
Avatar for rbnphlp
rbnphlp
11
Loz17
Sorry, my typo. I got 1-(-x)2

But won't that go to 1 + x2?

nope, try putting in your calculator (-2)^2(with the brackets)
square of anything is always positive
(-x)^2=x^2
Reply 4
Avatar for Stephens
Stephens
Loz17
f(x) = -x, g(x) = 1-x2

gf(x) = g(-x)

=>-(1-x)2

What have I done wrong? I'm trying to find ranges using this and any range I get from the domain is wrong :frown:

I've never liked these :frown:


Place -x into the g(x) function, you should get:

1-(-x)2

instead of -(1-x)2?

P.s, that will simplify to 1-x2
Reply 5
Avatar for LadySmythe
LadySmythe
OP
19
rbnphlp
nope, try putting in your calculator (-2)^2(with the brackets)


Ahh ********, how stupid of me :p:

Thank you :biggrin:
Reply 6
Avatar for maxfire
maxfire
14
Loz17
f(x) = -x, g(x) = 1-x2

gf(x) = g(-x)

=>1-(-x)2

What have I done wrong? I'm trying to find ranges using this and any range I get from the domain is wrong :frown:

I've never liked these :frown:


[br][br][br][br]gf(x)=1−(−x)2=1−x2[br][br][br][br][br][br]gf(x) = 1-(-x)^2 = 1 - x^2[br][br]

The range for gf(x) is 1≥x 1 \geq x

Is this what you wanted?
Reply 7
Avatar for LadySmythe
LadySmythe
OP
19
Yea, well I was just subbing domains in, as its -2 to 2 inclusive (I don't know latex :frown:)

But I have it now :smile:

Thank you all
Reply 8
Avatar for rbnphlp
rbnphlp
11
maxfire
[br][br][br][br]gf(x)=1−(−x)2=1−x2[br][br][br][br][br][br]gf(x) = 1-(-x)^2 = 1 - x^2[br][br]
]
The range for gf(x) is 1≥x 1 \geq x

Is this what you wanted?

you mean 1≥f(x) 1 \geq f(x)
Reply 9
Avatar for maxfire
maxfire
14
rbnphlp
you mean 1≥f(x) 1 \geq f(x)

yeah whoops.
Reply 10
Avatar for LadySmythe
LadySmythe
OP
19
One more quesiton, if thats ok? More of a confidence thing :frown:

f(x) and g(x) same as OP, h(x) = |x|

Is fgh(x) -(1-|x|)2 or am I making the same mistake as last time?
Reply 11
Avatar for rbnphlp
rbnphlp
11
Loz17
One more quesiton, if thats ok? More of a confidence thing :frown:

f(x) and g(x) same as OP, h(x) = |x|

Is fgh(x) -(1-|x|)2 or am I making the same mistake as last time?

just a small mistake it should have been −(1−∣x∣2)-(1-|x|^2)

can you see why?
Reply 12
Avatar for LadySmythe
LadySmythe
OP
19
rbnphlp
just a small mistake it should have -(1-(x^2))


I wasn't sure about that.

Thanks again :smile:

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