Let f(x)=2x−3. Find the inverse function f−1. Verify that f(f−1(x))=x.
Sketch the graph of f(x)=(12)x+2.
Solve the equation log5(x−1)+log5(x−2)=3log56–√3.
Express
logaxyz−−√−−−−−√3
in terms of logarithms of x, y, and z.
Solve the inequality xx−2≥1.
The current I in an electric circuit is given by
I=VR(1−e−0.3t).
Use natural logarithms to solve for t.
In Problems 9–12, solve each system of equations.
{1.4x0.4x−+0.5y1.1y==1.34.1
⎧⎩⎨⎪⎪2xx−3x+−+y2y4y−+−4z3zz===34−2
{yy−log(x+3)==2−logx1
{y3x2+8y2==x2−18
Find the determinant of the matrix ⎡⎣⎢123456789⎤⎦⎥.
Use Cramer’s Rule to solve the system of equations.
{2x−3y5x+7y==−41
Find the inverse of the matrix A=[3−5−24].
Find an equation of the line that passes through the point of intersection of the lines x+2y−3=0 and 3x+4y−5=0 and that is perpendicular to the line x−3y+5=0. Write your answer in slope–intercept form.
Solve the equation 2x4−5x2+3=0.
In Problems 18–20, an equation of a conic section is given. Identify the conic and sketch its graph.
x2−y2=−4
9x2+9y2=144
Sketch the graph of the rational function f(x)=xx2−16.