Answer:
a = [tex]\frac{1}{2}[/tex] , b = 5, and [tex]\frac{2b}{a}[/tex] = 20
Step-by-step explanation:
f(x) = - x² + b, x ≤ 0 You would use this equation for f(-2). Since -2 is less than 0.
f(x) = - x² + b, x ≤ 0 ← You can ignore the x ≤ 0 part.
f(-2) = - (-2)² + b Input the value -2 as x. The question states that f(-2) =1.
1 = - (-2)² + b So switch f(-2) with 1 on the left side only.
1 = - (4) + b Simplify. Do the exponents first, so (-2)² = 4.
1 = - 4 + b
+4 +4 Do inverse operations
5 = b
Next,
f(x) = 2ax +3, x > 0 You would use his equation for f(2). Since 2 is greater than 0.
f(x) = 2ax +3, x > 0 ← You can ignore the x > 0 part.
f(2) = 2a(2) + 3 Input the value 2 as x.
f(2) = 4a +3 Simplify. The equation states f(2) = 5. So switch f(2) with 5
5 = 4a +3 on the left side only.
-3 - 3 Do inverse operations
2 = 4a
[tex]\frac{2}{4}[/tex] = [tex]\frac{4a}{4}[/tex] Divide 4 on both sides to isolate the variable a
[tex]\frac{2}{4}[/tex] = a Simplify
[tex]\frac{1}{2}[/tex] = a
Then,
The second part says to find [tex]\frac{2b}{a}[/tex]
[tex]\frac{2b}{a}[/tex]
[tex]\frac{2(5)}{(\frac{1}{2}) }[/tex] Input both the values of a and b
[tex]\frac{10}{\frac{1}{2} }[/tex] Simplify
20.
The answer for a is [tex]\frac{1}{2}[/tex], the answer for b is 5, and the answer for [tex]\frac{2b}{a}[/tex] is 20.
