Let f(x) = StartFraction x squared minus 5 x + 4 Over x minus 1 EndFraction and g(x) = 2 Superscript x minus 3. For which value of x does f(g(x)) have a discontinuity?

9514 1404 393

  x=1

Step-by-step explanation:

The function f(x) is undefined where its denominator (x+1) is zero. That will be the case for x=-1.

The composition f(g(x)) will give f(x) an argument of -1 when g(x) = -1. That will be the case when ...

  2^x -3 = -1

  2^x = 2 . . . . . add 3

  x = 1 . . . . . . match exponents

f(g(x)) will have a discontinuity at x = 1.

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05