Work shown please.. I need help with this topic.
1 answer:
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For this case we have the following polynomial:
We make the following change of variables:
Rewriting we have
Factoring the second order polynomial we have:
Then, returning the change we have:
Finally, we factor the expression in the parentheses of the second term:
Answer:
the completely factored form is:
1/3 ln(<em>x</em>) + ln(2) - ln(3) = 3
Recall that , so
ln(<em>x</em> ¹ʹ³) + ln(2) - ln(3) = 3
Condense the left side by using sum and difference properties of logarithms:
Then
ln(2/3 <em>x</em> ¹ʹ³) = 3
Take the exponential of both sides; that is, write both sides as powers of the constant <em>e</em>. (I'm using exp(<em>x</em>) = <em>e</em> ˣ so I can write it all in one line.)
exp(ln(2/3 <em>x</em> ¹ʹ³)) = exp(3)
Now exp(ln(<em>x</em>)) = <em>x </em>for all <em>x</em>, so this simplifies to
2/3 <em>x</em> ¹ʹ³ = exp(3)
Now solve for <em>x</em>. Multiply both sides by 3/2 :
3/2 × 2/3 <em>x</em> ¹ʹ³ = 3/2 exp(3)
<em>x</em> ¹ʹ³ = 3/2 exp(3)
Raise both sides to the power of 3:
(<em>x</em> ¹ʹ³)³ = (3/2 exp(3))³
<em>x</em> = 3³/2³ exp(3×3)
<em>x</em> = 27/8 exp(9)
which is the same as
<em>x</em> = 27/8 <em>e</em> ⁹
Answer:
f[g(4)] = 4
Step-by-step explanation:
Given table:
f[g(4)] is a composite function.
When calculating <u>composite functions</u>, always work from inside the brackets out.
Begin with g(4): g(4) is the value of function g(x) when x = 4.
From inspection of the given table, g(4) = -6
Therefore, f[g(4)] = f(-6)
f(-6) is the value of function f(x) when x = -6.
From inspection of the given table, f(-6) = 4
Therefore, f[g(4)] = 4