Questions in mathematics

Questions in mathematics

[Done] Function \( f(x) = ax^{2} + bx + c \), where \( a, b, \) and \( c \) are constants. Define functions \( g \) and \( h \) as follows: \[ g(x) = f(x+1) - f(x) \] \[ h(x) = g(x+1) - g(x) \] Find the algebraic form of \( h(x) \). Can anyone explain how to make it step by step?

[Done] Functions \( f(x) \) and \( g(x) \) are both increasing. In addition, the range of \( g \) is in the domain of \( f \). Prove that the composite function \( f(g(x)) \) is increasing.

[Done] Solve the equation: \[ \log_8(2-5x) = \log_8(-4x+3) \]

[Done] If \( f(3) = 15 \) and \( f(5) = 45 \), which of the following could be \( f(x) \)?

[Done] How do you solve \(13 \frac{5}{9} - 8 \frac{1}{6}\)?

[Done] Find the radii of the circles satisfying the two requirements: (a) The circles are in the second quadrant and tangent to both axes. (b) Point \((-4, 4)\) is on their circumferences.

[Done] How do I write the equation \(9x - 6y = -72\) in slope-intercept form?

[Done] Find an equation of the line satisfying the given conditions: Through (6, 4); perpendicular to [tex]3X + 5Y = 38[/tex].

[Done] Give the values of \(a\), \(b\), and \(c\) needed to write the equation's general form. \(\frac{1}{4}x^2 + 5 = 0\)

[Done] What is the area of a sector of a circle with an arc measure of 45 degrees and a radius of 4?