Semester 1 Review Core- Part 1

Front

What is the inverse of the function f(x) = 5x - 8?

Back

The inverse is f^{-1}(x) = \frac{1}{5}x + \frac{8}{5}.

Front

How do you solve the equation 7^x - 13 = 2222 for x?

Back

x = 3.963.

Front

What is the limit of f(x) = \frac{42x^2}{7x^2 + 2} as x approaches ±∞?

Back

The limit is 6.

Front

What is the value of x if x = 30.256°?

Back

x = 30.256°.

Front

What is the correct expression for x in terms of sine?

Back

x = \frac{14}{\sin54°}.

Front

Define the concept of an inverse function.

Back

An inverse function reverses the operation of the original function, such that if f(x) = y, then f^{-1}(y) = x.

Front

What is the general method to find the inverse of a function?

Back

To find the inverse, swap x and y in the equation and solve for y.

Front

What is the significance of the horizontal line test in relation to functions?

Back

If a horizontal line intersects the graph of a function more than once, the function does not have an inverse.

Front

What is the definition of a limit in calculus?

Back

A limit is the value that a function approaches as the input approaches a certain point.

Front

Explain the concept of exponential equations.

Back

Exponential equations are equations in which variables appear as exponents, often solved using logarithms.