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Anastasy [175]
3 years ago
12

For the function F defined by F(x)=x2−2x+4, find F(−2).

Mathematics
2 answers:
Kruka [31]3 years ago
4 0

Answer:

12

Step-by-step explanation:

x^2-2x+4  replace -2 for x

-2^2-2(-2)+4

4+4+4

12

MAVERICK [17]3 years ago
3 0

Answer:

F(-2) = 12

Step-by-step explanation:

F(-2) = (-2)²- 2(-2) + 4

= 4 - (-4) + 4

= 4 + 4 + 4

= 12

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Given

a\sqrt{x+b}+c=d

we have

\sqrt{x+b}=\dfrac{d-c}{a}

Squaring both sides, we have

x+b=\dfrac{(d-c)^2}{a^2}

And finally

x=\dfrac{(d-c)^2}{a^2}-b

Note that, when we square both sides, we have to assume that

\dfrac{d-c}{a}>0

because we're assuming that this fraction equals a square root, which is positive.

So, if that fraction is positive you'll actually have roots: choose

a=1,\ b=0,\ c=2,\ d=6

and you'll have

\sqrt{x}+2=6 \iff \sqrt{x}=4 \iff x=16

Which is a valid solution. If, instead, the fraction is negative, you'll have extraneous roots: choose

a=1,\ b=0,\ c=10,\ d=4

and you'll have

\sqrt{x}+10=4 \iff \sqrt{x}=-6

Squaring both sides (and here's the mistake!!) you'd have

x=36

which is not a solution for the equation, if we plug it in we have

\sqrt{x}+10=4 \implies \sqrt{36}+10=4 \implies 6+10=4

Which is clearly false

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3 years ago
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Answer:

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Step-by-step explanation:

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