Answer:
g(f(2)) = 41
b)41
Step-by-step explanation:
g(f(2)) = 41
f(2)= 2(2²) + 5 = 13
So g(f(2)) → g(n = 13)
g(n = 13)→ 3(13) + 2 = 41
Answer:
Cannot be found with information given.
Step-by-step explanation:
Is there more information you failed to provide?
Step-by-step explanation:
f(x) + n - move the graph n units up
f(x) - n - move the graph n units down
f(x + n) - move the graph n units to the left
f(x - n) - move the graph n units to the right
====================================================
We have f(x) = 2ˣ.
g(x) = f(x) + 1 - move the graph of f(x) one unit up.
<em>(look at the picture)</em>
Answer:
Solve by factoring.
1. 2x^2+9x+26=-4x+5
2x²+9x+4x+26-5=0
2x²+13x+21=0
doing middle term factorization
2x²+7x+6x+21=0
x(2x+7)+3(2x+7)=0
<u>(</u><u>2</u><u>x</u><u>+</u><u>7</u><u>)</u><u>(</u><u>x</u><u>+</u><u>3</u><u>)</u><u>=</u><u>0</u>
<u>either</u>
<u>x</u><u>=</u><u>-</u><u>7</u><u>/</u><u>2</u>
<u>or</u>
<u>x</u><u>=</u><u>-</u><u>3</u><u>.</u>
2.
3x^2-6x-4=0
comparing above equation with ax²+bx+c=0
we get
a=3
b=-6
c=-4
By using quadratic equation
x=![\frac{ - b±\sqrt{ {b}^{2} - 4ac } }{2a}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20-%20b%C2%B1%5Csqrt%7B%20%7Bb%7D%5E%7B2%7D%20-%204ac%20%7D%20%7D%7B2a%7D%20)
Substituting value
x=![\frac{ 6±\sqrt{ {-6}^{2} - 4*3*-4 }}{2*-4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%206%C2%B1%5Csqrt%7B%20%7B-6%7D%5E%7B2%7D%20-%204%2A3%2A-4%20%7D%7D%7B2%2A-4%7D%20)
x=![\frac{ 6±\sqrt{ {84}}}{-8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%206%C2%B1%5Csqrt%7B%20%7B84%7D%7D%7D%7B-8%7D%20)
x=![\frac{ 6±2\sqrt{ {21}}}{-8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%206%C2%B12%5Csqrt%7B%20%7B21%7D%7D%7D%7B-8%7D%20)
-8x=6±2√21
taking positive
-8x=6+2√21
x=![\frac{6+2√21}{-8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B6%2B2%E2%88%9A21%7D%7B-8%7D%20)
x=-![\frac{3+√21}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%2B%E2%88%9A21%7D%7B4%7D%20)
taking negative
-8x=6-2√21
x=![\frac{6-2√21}{-8}](https://tex.z-dn.net/?f=%20%5Cfrac%7B6-2%E2%88%9A21%7D%7B-8%7D%20)
x=-![\frac{3-√21}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3-%E2%88%9A21%7D%7B4%7D%20)