F(x) = bx and g(x) = logb x are inverse functions. Explain why each of the following are true

1. A translation of function f is f1(x) = b(x – h). It is equivalent to a vertical stretch or vertical compression of function f.

2. The inverse of f1(x) = b(x – h) is equivalent to a translation ofg.

3. The inverse of f1(x) = b(x – h) is not equivalent to a vertical stretch or vertical compression of g.

4. The function h(x) = logc x is a vertical stretch or compression of g or of its reflection –g. Read this as “negative g”.

please need help

Evaluate 8x2 + 9x − 1 2x3 + 3x2 − 2x dx. solution since the degree of the numerator is less than the degree of the denominator, we don't need to divide. we factor the denominator as 2x3 + 3x2 − 2x = x(2x2 + 3x − 2) = x(2x − 1)(x + 2). since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form† 8x2 + 9x − 1 x(2x − 1)(x + 2) = correct: your answer is correct. to determine the values of a, b, and c, we multiply both sides of this equation by the product of the denominators, x(2x − 1)(x + 2), obtaining 8x2 + 9x − 1 = a correct: your answer is correct. (x + 2) + bx(x + 2) + cx(2x − 1).