What is the measure of angle x?
1 answer:
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Answer:
The inverse of f(x) is (x) = ±
+
Step-by-step explanation:
To find the inverse of the quadratic function f(x) = ax² + bx + c, you should put it in the vertex form f(x) = a(x - h)² + k, where
- h =
- k is the vlue f at x = h
∵ f(x) = 3x² - 3x - 2
→ Compare it with the 1st form above to find a and b
∴ a = 3 and b = -3
→ Use the rule of h to find it
∵ h = =
=
∴ h =
→ Substitute x by the value of h in f to find k
∵ k = 3( )² - 3(
) - 2
∴ k =
→ Substitute the values of a, h, and k in the vertex form above
∵ f(x) = 3(x - )² +
∴ f(x) = 3(x - )² -
Now let us find the inverse of f(x)
∵ f(x) = y
∴ y = 3(x - )² -
→ Switch x and y
∵ x = 3(y - )² -
→ Add to both sides
∴ x + = 3(y -
)²
→ Divide both sides by 3
∵ = (y -
)²
→ Take √ for both sides
∴ ± = y -
→ Add to both sides
∴ ± +
= y
→ Replace y by (x)
∴ (x) = ±
+
∴ The inverse of f(x) is (x) = ±
+
Answer:
The equation of the line is y = 2x - 3
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
- m is the slope of the line,
- b is the y-intercept (value y at x = 0)
Let us take two points on the line to find its equation
∵ Points (3, 3) and (0, -3) lie on the line
∴ x1 = 3 and y1 = 3
∴ x2 = 0 and y2 = -3
→ Use the rule of the slope above to find m
∵
∴ m = 2
→ Substitute its value in the form of the equation above
∴ y = 2x + b
∵ b is the value of y at x = 0
∵ y = -3 at x = 0
∴ b = -3
→ Substitute it in the equation above
∴ y = 2x + -3
→ Remember (+)(-) = (-)
∴ y = 2x - 3
∴ The equation of the line is y = 2x - 3
Answer: 4p^2-2p
Step-by-step explanation:
