topic badge
India
Class XI

Intersections of graphs by other methods II

Interactive practice questions

Michael is going to use the point of intersection of graphs to find an approximation to the positive solution of $\log\left(x\right)-1=-x+5$log(x)1=x+5.

a

One of the graphs is $f\left(x\right)=\log\left(x\right)-1$f(x)=log(x)1. What function $g\left(x\right)$g(x) should the other graph be of?

b

The graph of $f\left(x\right)$f(x) has been provided. On the same set of axes, graph $g\left(x\right)=-x+5$g(x)=x+5.

Loading Graph...
c

Between which two values does the solution of the equation lie? There may be more than one solution.

$x=4$x=4 and $x=9$x=9

A

$x=2$x=2 and $x=5$x=5

B

$x=6$x=6 and $x=7$x=7

C

$x=5$x=5 and $x=6$x=6

D
Easy
1min

Consider the function $f\left(x\right)=\log_2\left(x+1\right)$f(x)=log2(x+1).

Easy
1min

Consider the functions $f\left(x\right)=x^3+2x^2$f(x)=x3+2x2 and $g\left(x\right)=x+4$g(x)=x+4.

Medium
2min

The populations of two competing species of animals is given by $f\left(t\right)=215t+3$f(t)=215t+3 and $g\left(t\right)=\frac{1}{t-3}$g(t)=1t3, where $f\left(t\right)$f(t) and $g\left(t\right)$g(t) represent the respective populations $t$t years from now. Jenny is looking to determine approximately when their populations will be equal.

Medium
4min
Sign up to access Practice Questions
Get full access to our content with a Mathspace account

Outcomes

11.SF.RF.2

Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special kind of relation from one set to another. Pictorial representation of a function, domain, co-domain and range of a function. Real valued function of the real variable, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum and greatest integer functions with their graphs. Sum, difference, product and quotients of functions.

What is Mathspace

About Mathspace