An equation that shows the relationship of 30% of x is 40
2 answers:
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Solve for <em>x</em> when √(<em>x</em> ² - 4) = 1 :
√(<em>x</em> ² - 4) = 1
<em>x</em> ² - 4 = 1
<em>x</em> ² = 5
<em>x</em> = ±√5
We're looking at <em>x </em>≤ 0, so we take the negative square root, <em>x</em> = -√5.
This means <em>f</em> (-√5) = 1, or in terms of the inverse of <em>f</em>, we have <em>f</em> ⁻¹(1) = -√5.
Now apply the inverse function theorem:
If <em>f(a)</em> = <em>b</em>, then (<em>f</em> ⁻¹)'(<em>b</em>) = 1 / <em>f '(a)</em>.
We have
<em>f(x)</em> = √(<em>x</em> ² - 4) → <em>f '(x)</em> = <em>x</em> / √(<em>x</em> ² - 4)
So if <em>a</em> = -√5 and <em>b</em> = 1, we get
(<em>f</em> ⁻¹)'(1) = 1 / <em>f '</em> (-√5)
(<em>f</em> ⁻¹)'(1) = √((-√5)² - 4) / (-√5) = -1/√5
The sign must be negative; see the attached plot, and take note of the negatively-sloped tangent line to the inverse of <em>f</em> at <em>x</em> = 1.
The complete question in the attached figure
we have that
f(x) = x²<span> + 1
g(x) = x – 4
step 1
find </span>(f o g)(x)
(f o g)(x)= (x - 4)² + 1(f o g)(x) = x² - 8x + 16 + 1
(f o g)(x) = x² - 8x + 17
step 2
find (f o g)(10)
(f o g)(10) = 10² - 8*(10) + 17
(f o g)(10 = 100 - 80 + 17
(f o g)(10)= 37
the answer is 37
we have that
f(x) = x²<span> + 1
g(x) = x – 4
step 1
find </span>(f o g)(x)
(f o g)(x)= (x - 4)² + 1(f o g)(x) = x² - 8x + 16 + 1
(f o g)(x) = x² - 8x + 17
step 2
find (f o g)(10)
(f o g)(10) = 10² - 8*(10) + 17
(f o g)(10 = 100 - 80 + 17
(f o g)(10)= 37
the answer is 37